Let f:[a,b]->R be a continuous and differentiable function on
(a,b). If f(x)>0 for all x in [a,b], what can we conclude about the existence of c in
(a,b) such that f
(b)=f
(a)exp(
(b-a)(f^(')
(c))/(f)?
A. There exists a c in
(a,b) such that f
(b)=f
(a)exp(
(b-a)(f^(')
(c))/(f)
B. There does not exist a c in
(a,b) such that f
(b)=f
(a)exp(
(b-a)(f^(')
(c))/(f)
C. The existence of c in
(a,b) such that f
(b)=f
(a)exp(
(b-a)(f^(')
(c))/(f) depends on the specific values of a, b, and f
D. None of the above